In a fluid jet weaving loom, a so-called weft yarn grasping apparatus is employed for alternately grasping and releasing the weft yarn which is to be inserted in the shed of the warp yarns. Widely used grasping apparatus are of a type comprising a stationary disc member and a movable disc member which are axially aligned to be contactable with and separable from each other, the movable disc member being reciprocably movable with respect to the stationary disc member so as to intermittently form a clearance through which the weft yarn is passed. In grasping of the weft yarn, the movable disc member is brought into contact with the stationary disc member to strongly press the weft yarn to the stationary disc member. Upon releasing of the weft yarn, the movable disc member is completely separated from the stationary disc member to form a large clearance therebetween. Usually, the movable disc member is arranged rotatable axially relative to the stationary disc member and the contacting surfaces of the stationary and movable disc members are substantially entirely flat. In this type grasping apparatus, however, it inevitably occurs, upon long time usage thereof, that the peripheral portions of these disc members are greatly worn out with a result that the actual grasping of the weft yarn is made only by generally central portions of these disc members. The grasping ability of the apparatus is thus reduced causing the failure of picking of the weft yarn into the shed.